In the previous post we formed notions of matrix, determinants, rank of a matrix and system of linear equations. We also mentioned the fundamental theorem on solution of system of linear equations which tells us the importance of rank in deciding the nature of solution of such systems of equations. It is now time to establish the theorem and to do that we start by defining a systematic method of solving such systems of linear equations.

In this post I will be talking about the simple and beautiful concept of matrices. In particular I will discuss about the rank of a matrix and its usage in solving system of linear equations. In order to keep the post to a reasonable length I will not dwell upon the usual operations on matrices and assume that the reader is familiar with them, but a paragraph or two about these operations definitely makes sense.